(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     10584,        343]
NotebookOptionsPosition[      7224,        246]
NotebookOutlinePosition[      9886,        317]
CellTagsIndexPosition[      9769,        311]
WindowTitle->TrickMandelstam
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[
     ActionMenuBox[
      FrameBox[
       InterpretationBox[Cell[TextData[{
         "URL",
         StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
          StripOnInput->False]
        }]],
        TextCell[
         Row[{"URL", 
           Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
       StripOnInput->False], {"\<\"FeynCalc/ref/TrickMandelstam\"\>":>
      None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
      Module[{DocumentationSearch`Private`nb$}, 
       DocumentationSearch`Private`nb$ = NotebookPut[
          Notebook[{
            Cell["FeynCalc/ref/TrickMandelstam"]}, Visible -> False]]; 
       SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
       FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
       NotebookClose[DocumentationSearch`Private`nb$]; Null], 
      Delimiter, "\<\"Copy web URL\"\>":>
      Module[{DocumentationSearch`Private`nb$}, 
       DocumentationSearch`Private`nb$ = NotebookPut[
          Notebook[{
            Cell[
             BoxData[
              MakeBoxes[
               Hyperlink[
               "http://reference.wolfram.com/language/FeynCalc/ref/\
TrickMandelstam.html"], StandardForm]], "Input", TextClipboardType -> 
             "PlainText"]}, Visible -> False]]; 
       SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
       FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
       NotebookClose[DocumentationSearch`Private`nb$]; 
       Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
        NotebookLocate[{
          URL[
           StringJoin[
            If[
             TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$278817], 
             "http://reference.wolfram.com/system-modeler/", 
             "http://reference.wolfram.com/language/"], 
            "FeynCalc/ref/TrickMandelstam", ".html"]], None}]}]},
      Appearance->None,
      MenuAppearance->Automatic,
      MenuStyle->"URLMenu"]],
     LineSpacing->{1.4, 0}]], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["TrickMandelstam", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"TrickMandelstam", "[", 
       RowBox[{"expr", ",", " ", 
        RowBox[{"{", 
         RowBox[{"s", ",", " ", "t", ",", " ", "u", ",", 
          RowBox[{
           RowBox[{"m1", "^", "2"}], "+", 
           RowBox[{"m2", "^", "2"}], "+", 
           RowBox[{"m3", "^", "2"}], "+", 
           RowBox[{"m4", "^", "2"}]}]}], "}"}]}], "]"}]], "InlineFormula"],
     " \[LineSeparator]simplifies all sums in expr so that one of the \
Mandelstam variables s, t or u is eliminated by the relation ",
     StyleBox["s",
      FontSlant->"Italic"],
     " + ",
     StyleBox["t",
      FontSlant->"Italic"],
     " + ",
     StyleBox["u",
      FontSlant->"Italic"],
     " = ",
     Cell[BoxData[
      FormBox[
       SubsuperscriptBox[
        StyleBox["m",
         FontSlant->"Italic"], "1", "2"], TraditionalForm]]],
     " + ",
     Cell[BoxData[
      FormBox[
       SubsuperscriptBox["m", "2", "2"], TraditionalForm]]],
     "+ ",
     Cell[BoxData[
      FormBox[
       SubsuperscriptBox["m", "3", "2"], TraditionalForm]]],
     "+ ",
     Cell[BoxData[
      FormBox[
       SubsuperscriptBox["m", "4", "2"], TraditionalForm]]],
     " . The trick is that the resulting sum has the most short number of \
terms."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->1671052356],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->756444211],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"TrickMandelstam", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"s", "+", "t", "-", "u"}], ")"}], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"2", 
        SubsuperscriptBox["M", "W", "2"]}], "-", "t", "-", "u"}], ")"}]}], 
    ",", 
    RowBox[{"{", 
     RowBox[{"s", ",", "t", ",", "u", ",", 
      RowBox[{"2", 
       SubsuperscriptBox["M", "W", "2"]}]}], "}"}]}], "]"}], "//", 
  "Factor2"}]], "Input",
 CellTags->"TrickMandelstam",
 CellLabel->"In[1]:=",
 CellID->576381697],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", "2"}], " ", "s", " ", 
   RowBox[{"(", 
    RowBox[{"u", "-", 
     SubsuperscriptBox["M", "W", "2"]}], ")"}]}], TraditionalForm]], "Output",\

 ImageSize->{107, 21},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"TrickMandelstam",
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TrickMandelstam", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"M", "^", "2"}], " ", "s"}], " ", "-", " ", 
    RowBox[{"s", "^", "2"}], " ", "+", " ", 
    RowBox[{
     RowBox[{"M", "^", "2"}], " ", "t"}], " ", "-", " ", "st", " ", "+", " ", 
    
    RowBox[{
     RowBox[{"M", "^", "2"}], " ", "u"}], " ", "-", " ", "su"}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"s", ",", "t", ",", "u", ",", 
     RowBox[{"2", 
      RowBox[{"M", "^", "2"}]}]}], "}"}]}], "]"}]], "Input",
 CellTags->"TrickMandelstam",
 CellLabel->"In[2]:=",
 CellID->2075024335],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    SuperscriptBox["M", "4"]}], "-", 
   SuperscriptBox["s", "2"], "-", "st", "-", "su"}], 
  TraditionalForm]], "Output",
 ImageSize->{131, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"TrickMandelstam",
 CellLabel->"Out[2]="]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"TrickMandelstam",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 12, 12.772960}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "TrickMandelstam[expr, {s, t, u, m1^2 + m2^2 + m3^2 + m4^2}] simplifies \
all sums in expr so that one of the Mandelstam variables s, t or u is \
eliminated by the relation s + t + u = m_1^2 + m_2^2+ m_3^2+ m_4^2 . The \
trick is that the resulting sum has the most short number of terms.", 
    "synonyms" -> {}, "tabletags" -> {}, "title" -> "TrickMandelstam", 
    "titlemodifier" -> "", "windowtitle" -> "TrickMandelstam", "type" -> 
    "Symbol", "uri" -> "FeynCalc/ref/TrickMandelstam"}, 
  "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[4696, 141, 388, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->1671052356]},
 "TrickMandelstam"->{
  Cell[5329, 170, 545, 19, 33, "Input",
   CellTags->"TrickMandelstam",
   CellID->576381697],
  Cell[5877, 191, 335, 12, 42, "Output",
   CellTags->"TrickMandelstam"],
  Cell[6249, 208, 586, 18, 45, "Input",
   CellTags->"TrickMandelstam",
   CellID->2075024335],
  Cell[6838, 228, 320, 11, 37, "Output",
   CellTags->"TrickMandelstam"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 9263, 293},
 {"TrickMandelstam", 9406, 297}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[587, 21, 2302, 53, 53, "AnchorBarGrid",
 CellID->1],
Cell[2892, 76, 292, 11, 45, "ObjectNameGrid"],
Cell[3187, 89, 1484, 48, 107, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[4696, 141, 388, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->1671052356],
Cell[CellGroupData[{
Cell[5109, 160, 195, 6, 26, "ExampleSection",
 CellID->756444211],
Cell[CellGroupData[{
Cell[5329, 170, 545, 19, 33, "Input",
 CellTags->"TrickMandelstam",
 CellID->576381697],
Cell[5877, 191, 335, 12, 42, "Output",
 CellTags->"TrickMandelstam"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6249, 208, 586, 18, 45, "Input",
 CellTags->"TrickMandelstam",
 CellID->2075024335],
Cell[6838, 228, 320, 11, 37, "Output",
 CellTags->"TrickMandelstam"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[7197, 244, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

